Parent to bone (by only rotation), or snap head to origin of other object
If I understand your question, you want to build an armature (in edit mode) in which the bone's head is exactly in the object origin location. To do so, select the object, press Shift S (Cursor to selected), then select the armature, go to edit mode, select the head of the desired bone, press Shift S (Selection to cursor). THEN parent the object to the bone (Ctrl P - Bone).